order	192
isoclinism	isoclinic class of #95⋊C₃
automorphism	Aut(G) = C₂×#4626⋊C₂ (order 768) · Inn(G) = C₄²⋊C₃ · Out(G) = C₂×D₄
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#95⋊C₃
unambiguous semidirect product	(C₂×#95)⋊C₃

Splittings

Fitting, Sylow	C₂×#95 ⋊ C₃
derived	#95 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂²	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃
Frattini	C₂³	C₂×A₄
Fitting	C₂×#95	C₃
socle	C₂⁴	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂²

75 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 14 points:

(1,2)(3,4,8)(5,10,14)(6,11,12)(7,9,13);(4,10,9,11)(5,6)(8,14)(12,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 189);